Method and system for merchandise hierarchy refinement by incorporation of product correlation

ABSTRACT

System, method and computer program product for adjusting a representation of a merchandise hierarchy associated with an entity such as a retailer or wholesaler of products. Product correlation information discovered in that entity&#39;s customers&#39; shopping records are obtained and incorporated into an existing merchandise hierarchy with a constraint on the consistency with the existing hierarchy.

BACKGROUND

The present invention is related generally to hierarchical organizationof an entity's merchandise, i.e., product/inventory, and morespecifically, to a method and system for merchandise hierarchyrefinement by incorporating product correlation. More specifically, thepresent invention relates to a method and system of incorporatingproduct correlation information discovered in customers' shoppingprofiles (records) to adjust an existing merchandise hierarchy with aconstraint on the consistency with the existing hierarchy.

Merchandise hierarchy is a tree-like structure for organizingmerchandise categories and products of an entity, e.g., a productwholesaler/retailer. It plays a key role in the business decision-makingprocess. First, merchandise hierarchy is the base of management andoperation structure: departments are usually organized according to themerchandise hierarchy and are responsible for all business related butsub-categories and products under the category, e.g., procurement,forecasting, shelf layout, etc. Moreover, merchandise analytics atlevels defined in the hierarchy are the basis of business strategyadjustment, such as statistics, reporting, performance evaluation, etc.

Currently, there is no mechanism for incorporating customers' shoppingbehavior (e.g., a shopping profile or history) in such merchandiseanalytics. Such information is useful to facilitate improvement of thebusiness structure and make it truly customer-oriented.

SUMMARY

The present invention is a system and method for refining an entity'smerchandise hierarchy, particularly by generating a more comprehensivemerchandise hierarchy for an entity (e.g., a product retailer orwholesaler) that incorporates information representing the shoppingbehavior of customer(s).

According to one aspect of the invention, there is provided a method ofmerchandise hierarchy refinement comprising: extracting first datarepresenting a predetermined merchandise hierarchy and second datarepresenting transaction records having a plurality of transactionsrelated to a plurality of products; clustering the plurality of productsbased on the plurality of transactions; and updating the predeterminedmerchandise hierarchy representation based on the clustering, wherein aprogram using a processor unit performs one or more of the extracting,clustering and updating.

Further to this aspect of the invention, the step of clusteringcomprises: setting a current level of the merchandise hierarchy as abottom level of the merchandise hierarchy, initializing a new membershipmatrix to an existing membership matrix; applying a Genetic Algorithm tominimize an objective function, wherein in each step of the GeneticAlgorithm, a new generation group of the new membership matrix satisfiesa consistency constraint; repeating the initializing and applying at anext upper level of the current level until a next highest level of themerchandise hierarchy is reached; and outputting the new membershipmatrix.

The comprehensive merchandise hierarchy helps to improve the businessstructure and make it truly customer-oriented which will, in turn,increase customer's satisfaction, improve operational efficiency, andreduce the cost of management.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the present invention, and are incorporated in andconstitute a part of this specification. The drawings illustrateembodiments of the invention and, together with the description, serveto explaining the principles of the invention. In the drawings,

FIG. 1 illustrates an overview of the system and method for merchandisehierarchy refinement according to a preferred embodiment of the presentinvention;

FIG. 2 illustrates an example of a predefined merchandise hierarchy;

FIG. 3 illustrates an example of a transaction record data table;

FIG. 4 illustrates an example of the refined merchandise hierarchy basedon the transaction record data illustrated in FIG. 3, according to oneembodiment; and

FIG. 5 illustrates the flow chart for the method for the merchandisehierarchy refinement; and,

FIG. 6 illustrates an exemplary hardware configuration for implementingthe flow charts depicted in FIGS. 1 and 5 according to one embodiment ofthe present invention.

DETAILED DESCRIPTION

FIG. 1 illustrates an overview of a system and computer-implementedmethod 100 for merchandise hierarchy refinement according to a preferredembodiment of the present invention. In the system 100, there isemployed at least three processing modules: a data extraction module101, a cluster model with consistency constraints module 102, and amerchandise hierarchy updater module 103.

The data extraction module (101) receives two data feeds: a first datainput 11 for receiving data representing a predefined merchandisehierarchy; and, second data input 12 for receiving customers'transaction records. As will be described, the received customertransaction records are preprocessed by the data extraction module 101to obtain item similarity.

The cluster model with consistency restraints 102 performs clusteringover the items of each level of merchandise hierarchy by addingconsistency restraints based on a ratio of mutual information.

The merchandise hierarchy updater 103 performs updating of thecorresponding items and updating of the links between the correspondinglevels of merchandise hierarchy.

FIG. 2 illustrates an example of a predefined merchandise hierarchy 200having a tree-like structure that comprises the first data input 11 tothe data extraction module (101). In particular, any common hierarchicaltree representation can be input that includes representation of nodes,e.g., with pointers to their children, their parents, or both, or asitems in an array with relationships between them determined by theirpositions in the array is input. For purposes of discussion, themerchandise hierarchy 200 is provided for an example merchandise retailentity, e.g., “J-mart,” which may be a chain of retail stores. The chainJ-Mart (201) is arranged in a hierarchical manner with the top node ofthe tree 201 indicating the retail entity (chain). The retail entity atthe top node is divided into several departments 202, indicated as childnodes 202 a, 202 b, 202 c. As shown in FIG. 2, for example, a firstchild node represents a Shoes department (202 a). Departments in thehierarchy are further divided into classes 203. For example, as shown inFIG. 2, the Shoes department (202 a) is further divided into classesincluding a Men's summer shoes class (203 a). Classes 203 in thehierarchy are further divided into items 204. For example, Men's summershoes class 203 a in the hierarchy includes products of merchandise suchas the walker shoes (204 a).

FIG. 3 presents an example of a transaction record data table 300 thatcomprises the second data input 12 to the data extraction module (101).FIG. 3 in particular gives the attributes of a transaction record, andthese records with attributes are stored into a database or like memorystorage structure. The example table includes main attribute columns:Transaction ID (301) and Merchandise Category (302). MerchandiseCategory column 302 includes items or products of the retailer that mayhave been subject to purchase in particular customers' transactions(indicated by the Transaction ID). For example, the merchandise categoryshown in FIG. 3 indicates three products: bread (303), milk (304) andfruit (305) for the merchandise category. In the transaction record datatable 300, for each transaction, a ‘1’ entry in the column representsthat the product is bought and ‘0’ represents that the product is notbought. Note that the times any two products are bought together arecounted as similarities between the two products. In this example table,it can be seen that milk and bread are bought together 2 times, milk andfruit are bought together 2 times, and bread and fruit are boughttogether 1 time. Intuitively, the more times two products are boughttogether, the more they complement each other.

As mentioned, the data extractor module 101 preprocesses the receivedcustomer transaction records to generate item similarities, i.e., asimilarities count.

This similarities count data is input to the cluster model withconsistency constraints module (102) in FIG. 1. The similarities arereal numbers without complex data structures, and the manner in whichthey are calculated is explained in greater detail herein below. Thecluster model with consistency constraints (102) in FIG. 1 performsclustering over products of each level of the merchandise hierarchy byadding consistency constraints based on a ratio of mutual informationbetween the predefined merchandise hierarchy and the refined hierarchythat reflects their difference. Thus, in this phase (102), themerchandise hierarchy has been refined.

First, the notations used in the clustering model implemented by theconsistency constraints module (102) are introduced as follows:

N=number of products (e.g., N_(i+1) is the number of products of thelevel i+1 that is determined by predefined merchandise hierarchy);

M=number of original categories;

K=number of new categories;

W={W_(ij)}=N×N similarity matrix;

D=diag{d₁, . . . , d_(N)}, where d₁=Σ_(j)W_(ij);

C=N×K new member matrix, wherein C_(i)=ith row of C;

C^(T) is a transpose matrix of C,

T=existing category labels defined by the existing hierarchy (e.g.,Tij=1 whenever product i belongs to category j. Otherwise, Tij=0. Thesize of matrix T is subject to the existing hierarchy that may bedifferent from the size of C);

p_(ij)=fraction of sales volume of products in new category i andexisting category j;

p_(i)*=Σ_(j)p_(ij)=fraction of sales volume of products in new categoryI;

p*_(j)=Σ_(i)p_(ij)=fraction of sales volume of products in existingcategory j;

$\mspace{20mu}{{{H(T)} = {{- {\sum\limits_{j = 1}^{M}{p_{j}^{*}{\log\left( p_{j}^{*} \right)}}}} = {{Shannon}\mspace{14mu}{entropy}\mspace{14mu}{of}\mspace{14mu} T}}};}$${{I\left( {C,T} \right)} = {{\sum\limits_{i = 1}^{K}{\sum\limits_{j = 1}^{M}{p_{ij}{\log\left( \frac{p_{ij}}{p_{i}^{*} \times p_{j}^{*}} \right)}}}} = {{mutual}\mspace{14mu}{information}\mspace{14mu}{between}\mspace{14mu} C\mspace{14mu}{and}\mspace{14mu} T}}};$

Q(C,T)=H(T)/I(C,T)=ratio of mutual information;

η≧1=control parameter.

It is understood that data N, M, D, K, W, p, H( )I( )Q( ) are extractedfrom the transaction records.

Using the definitions given above, finding a clustering assignmentoperation is performed whereby each product is assigned a cluster label,i.e. the output matrix C, such that similar items have similarassignments is tantamount to finding a solution to the new member matrix“C” which satisfies the following objective function:

${{\min{\sum\limits_{i,{j = 1}}^{N}{W_{ij}{{C_{i} - {C\; j}}}^{2}}}} = {{trace}\left( {{C^{T}\left( {D - W} \right)}C} \right)}},$

such that Q(C,T)≦η.

The objective function which makes use of the complementary informationbetween products means that similar products have similar clusterassignments. A description of a clustering technique that can be used ispresented herein below in greater detail.

The consistency constraint leverages expertise to control the extent ofhierarchy change. It can be found that Q(C,T) is minimized to 1 if andonly if the sales distributions with the new and existing categories areidentical. The higher the confidence level of the predefined merchandisehierarchy, i.e., the confidence level that can be mirrored by parameterand adopted to only show the degree of belief in the predefinedmerchandise hierarchy, the smaller the value of η. In practice, theconfidence level of predefined hierarchy is determined by tuning thecontrol parameter η which is a presupposed positive constant based onthe expertise to predefined merchandise hierarchy (i.e. its confidencelevel) before clustering. Hence, for a given η the whole bottom-upprocess is performed once.

Accordingly, in one embodiment, an optimization algorithm is implementedfor the cluster model with the following consistency constraints:Initialization: C=T. The algorithm includes:

-   -   1. Applying a Genetic Algorithm (GA) (e.g., see reference to        Holland, John H entitled Adaptation in Natural and Artificial        Systems, University of Michigan Press, Ann Arbor (1975),        incorporated by reference herein) to minimize the objective        function. Generally, GA algorithms are implemented in a computer        simulation in which a population of abstract representations of        candidate solutions to an optimization problem evolves toward        better solutions. The evolution usually starts from a population        of randomly generated individuals (binary representation) and        happens in generations. In each generation (iteration), multiple        individuals are stochastically selected from the current        population based on their fitness (i.e. the corresponding value        of objective function), and modified (recombined and randomly        mutated) to form a new population that is then used in the next        iteration. Commonly, the algorithm terminates when either a        maximum number of generations has been produced, or a        satisfactory fitness level has been reached. However, slightly        different from the above original GA, in each iteration of the        present method, it is demanded that the new generation group of        variable C must satisfy the consistency constraints. Hence, in        each generation those individuals breaking consistency        constraints must be removed.    -   2. Output the final cluster assignments C, i.e., the matrix C is        just the structure output. Cij=1 means product i belongs to        category j and otherwise Cij=0. Therefore, the refined        merchandise hierarchy may be re-drawn in terms of C such as        described herein with respect to FIG. 4.

The final cluster assignments C are output to the Merchandise Hierarchyupdater (103) as shown in FIG. 1, which updates the clustering of thecorresponding items according to the result computed by the ClusterModel, and updates the links between the corresponding levels of themerchandise hierarchy such as the merchandise hierarchy 200 shown inFIG. 2.

FIG. 4 shows an example of updates 400 performed by the MerchandiseHierarchy Updater module 103. As shown in FIG. 4, the originalcategories in the middle level only included Staple food (401) and Dairy(402). After implementing the cluster modeling performed by module 102,besides two existing categories, a new category ‘Cluster 3’ (403) isgenerated according to cluster assignments. The new category containstwo products bread (404) and milk (405) that originally belong to theStaple food (401) and Dairy (402) respectively Here, MerchandiseHierarchy Updater performs three things: first, give Cluster 3 a title,e.g. Breakfast (406) that is in accordance with the meanings of breadand milk and create a new category node Breakfast; second, discard thelinks from bread to Staple food (401) and from milk to Dairy (402), andadd links from bread and milk to Breakfast (406); third, add a link fromBreakfast (406) to its upper level nodes, e.g. create a link fromBreakfast to Foodline (407).

In summary, a bottom-up strategy to adjust the predefined merchandisehierarchy is adopted. The method implementing the strategy in theMerchandise Hierarchy Updater module 103 is as follows:

-   -   1) choose a starting level in the existing hierarchy;    -   2) sequentially implement the three modules: the data extractor,        the cluster model with consistency constraints and the        merchandise hierarchy updater;    -   3) return to perform the second step on the upper category level        of the current level;    -   4) output the refined merchandise hierarchy until the next        highest level is reached.

FIG. 5 illustrates a flow chart for the method 450 for the merchandisehierarchy refinement according to the present invention. In step 455,given a hierarchy with n levels, the method includes: setting the bottomlevel as the current level (i.e. set current level as level i andinitialize i=1). In step 460, the clustering method is performed on thecurrent level i and the links between the current level i and the upperlevel i+1 are performed. In step 465, the links between the upper leveli+1 and the next upper level I+2 are updated. After the updates in step465, a determination is made as to whether the current value is the nexthighest level in step 470. If the current level is not the next highestlevel, then the upper level is set as the current level at 471 and theclustering updating in steps 460 and 465 are repeated; otherwise, therefined hierarchy is output at 475 and the process terminates. Theupdating of the predetermined merchandise hierarchy representation thusincludes adding a new node and corresponding link connecting the newnode to a parent node of said first lower or second next lower levelnode.

In one example, as a result of implementing the present invention, thecomprehensive merchandise hierarchy helps to improve the businessstructure and make it truly customer-oriented which will, in turn,increase customer's satisfaction, improve operational efficiency, andreduce the cost of management. For example, a new category may becreated for young mothers that often buy products for themselvestogether with products for their baby, and baby products are no longerseparately located in individual categories, such as baby milk in thediary department, or baby clothing in clothing department.

FIG. 6 illustrates an exemplary hardware configuration of a computingsystem 500 running and/or implementing the method steps in FIGS. 1 and5. The hardware configuration preferably has at least one processor orcentral processing unit (CPU) 511. The CPUs 511 are interconnected via asystem bus 512 to a random access memory (RAM) 514, read-only memory(ROM) 516, input/output (I/O) adapter 518 (for connecting peripheraldevices such as disk units 521 and tape drives 540 to the bus 512), userinterface adapter 522 (for connecting a keyboard 524, mouse 526, speaker528, microphone 532, and/or other user interface device to the bus 512),a communication adapter 534 for connecting the system 500 to a dataprocessing network, the Internet, an Intranet, a local area network(LAN), etc., and a display adapter 536 for connecting the bus 512 to adisplay device 538 and/or printer 539 (e.g., a digital printer of thelike).

Although the embodiments of the present invention have been described indetail, it should be understood that various changes and substitutionscan be made therein without departing from spirit and scope of theinventions as defined by the appended claims. Variations described forthe present invention can be realized in any combination desirable foreach particular application. Thus particular limitations, and/orembodiment enhancements described herein, which may have particularadvantages to a particular application need not be used for allapplications. Also, not all limitations need be implemented in methods,systems and/or apparatus including one or more concepts of the presentinvention.

The present invention can be realized in hardware, software, or acombination of hardware and software. A typical combination of hardwareand software could be a general purpose computer system with a computerprogram that, when being loaded and run, controls the computer systemsuch that it carries out the methods described herein. The presentinvention can also be embedded in a computer program product, whichcomprises all the features enabling the implementation of the methodsdescribed herein, and which—when loaded in a computer system—is able tocarry out these methods.

Computer program means or computer program in the present contextinclude any expression, in any language, code or notation, of a set ofinstructions intended to cause a system having an information processingcapability to perform a particular function either directly or afterconversion to another language, code or notation, and/or reproduction ina different material form.

Thus the invention includes an article of manufacture which comprises acomputer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the article of manufacture comprisescomputer readable program code means for causing a computer to effectthe steps of a method of this invention. Similarly, the presentinvention may be implemented as a computer program product comprising acomputer usable medium having computer readable program code meansembodied therein for causing a function described above. The computerreadable program code means in the computer program product comprisingcomputer readable program code means for causing a computer to affectone or more functions of this invention. Furthermore, the presentinvention may be implemented as a program storage device readable bymachine, such as a processing device, microprocessor, processor unit,etc., tangibly embodying a program of instructions operated by themachine to perform method steps for causing one or more functions ofthis invention.

The present invention may be implemented as a computer readable medium(e.g., a compact disc, a magnetic disk, a hard disk, an optical disk,solid state drive, digital versatile disc) embodying program computerinstructions (e.g., C, C++, Java, Assembly languages, Net, Binary code)run by a processor (e.g., Intel® Core™, IBM® PowerPC®) for causing acomputer to perform method steps of this invention. The presentinvention may include a method of deploying a computer program productincluding a program of instructions in a computer readable medium forone or more functions of this invention, wherein, when the program ofinstructions is run by a processor, the computer program productperforms the one or more of functions of this invention.

It is noted that the foregoing has outlined some of the more pertinentobjects and embodiments of the present invention. This invention may beused for many applications. Thus, although the description is made forparticular arrangements and methods, the intent and concept of theinvention is suitable and applicable to other arrangements andapplications. It will be clear to those skilled in the art thatmodifications to the disclosed embodiments can be effected withoutdeparting from the spirit and scope of the invention. The describedembodiments ought to be construed to be merely illustrative of some ofthe more prominent features and applications of the invention. Otherbeneficial results can be realized by applying the disclosed inventionin a different manner or modifying the invention in ways known to thosefamiliar with the art.

1. A method of merchandise hierarchy refinement, comprising: extractingfirst data from a predetermined merchandise hierarchy represented as atree data structure of nodes interconnected by links wherein one or moreproducts at a lowest level node of said hierarchy are assigned as beinga member of a category at an upper category level node of said hierarchyand include a link to that category level node, and second datarepresenting transaction records having a plurality of transactionsrelated to the plurality of products; clustering said plurality ofproducts based on said plurality of transactions in which a new clusteris generated relating to products of said plurality; and updating thepredetermined merchandise hierarchy representation based on saidclustering in which said products of said new cluster are assigned asbeing members of a new category level node, and a new link generated forconnecting the products and corresponding new category level node,wherein said clustering comprises: initializing a new membership matrixas representing categories and their member product assignmentsaccording to a lowest level of said predefined merchandise hierarchy;performing, via a computer simulation, an iterative process to minimizean objective function relating a similarity of complementary informationbetween said plurality of products, wherein at each iteration, assigningeach product to a cluster label such that similar items have similarassignments to update said new membership matrix and form a refinedmerchandise hierarchy that satisfies a consistency constraint based on aratio of mutual information representing a difference between thepredefined merchandise hierarchy and the refined merchandise hierarchy;repeating said initializing and performing at a next upper level until anext highest level of said refined merchandise hierarchy is reached; andoutputting said new membership matrix, wherein a program using aprocessor unit performs one or more of said extracting, clustering andupdating.
 2. The method of merchandise hierarchy refinement of claim 1,wherein said objective function is:${{\min{\sum\limits_{i,{j = 1}}^{N}{W_{ij}{{C_{i} - {C\; j}}}^{2}}}} = {{trace}\left( {{C^{T}\left( {D - W} \right)}C} \right)}},$wherein W={W_(ij)} is an N×N similarity matrix, D=diag{d₁, . . . ,d_(N)}, wherein d_(i)=Σ_(j)W_(ij), C is a N×K new member matrix, whereinC_(i)=ith row of C and Cj=jth row of C, C^(T) is a transpose matrix ofC, N is a number of products in a current level of said predeterminedmerchandise hierarchy, and K is a number of new categories in a currentlevel of said predetermined merchandise hierarchy.
 3. The method ofmerchandise hierarchy refinement of claim 2, wherein said consistencyconstraint based on a ratio of mutual information is computed as:$\mspace{20mu}{{{Q\left( {C,T} \right)} = {{H(T)}/{I\left( {C,T} \right)}}},{{{wherein}\mspace{14mu}{H(T)}} = {- {\sum\limits_{j = 1}^{M}{p_{j}^{*}{\log\left( p_{j}^{*} \right)}}}}},{{{I\left( {C,T} \right)} = {{\sum\limits_{i = 1}^{K}{\sum\limits_{j = 1}^{M}{p_{ij}{\log\left( \frac{p_{ij}}{p_{i}^{*} \times p_{j}^{*}} \right)}}}} = {{mutual}\mspace{14mu}{information}\mspace{14mu}{between}\mspace{14mu} C\mspace{14mu}{and}\mspace{14mu} T}}};}}$and, wherein C is a N×K new member matrix, T is an existing categorylabels matrix defined by the existing hierarchy, p_(ij) is a fraction ofsales volume of products in new category i and existing category j,p_(i)*=Σ_(j)p_(ij)=fraction of sales volume of products in new categoryi p*_(j)=Σ_(i)p_(ij)=fraction of sales volume of products in existingcategory j, N is a number of products in a current level of saidpredetermined merchandise hierarchy, M is a number of originalcategories in a current level of said predetermined merchandisehierarchy, and K is a number of new categories in a current level ofsaid predetermined merchandise hierarchy.
 4. The method of merchandisehierarchy refinement of claim 3, wherein said first data representingpredetermined merchandise hierarchy including said tree data structureincludes a top level node, representing a top of said hierarchy, and afirst lower hierarchy level including one or more first lower levelnodes connected to said top node by respective links, and a second lowerhierarchy level including one or more second lower level nodes connectedto a node of said first lower level nodes via links, said updating thepredetermined merchandise hierarchy representation comprising adding anew node and link connecting to a node of said first lower or secondnext lower level node.
 5. The method of merchandise hierarchy refinementof claim 4, wherein said new membership matrix output includes clusterassignments C used for updating the nodes and links in saidpredetermined merchandise hierarchy representation.
 6. The method asclaimed in Claim 1, wherein said iterative process includes applying aGenetic Algorithm.
 7. A computer program product for performingmerchandise hierarchy refinement, the computer program productcomprising: a tangible storage device readable by a processing circuitand storing instructions for operation by the processing circuit forperforming a method comprising: extracting first data from apredetermined merchandise hierarchy represented as a tree data structureof nodes interconnected by links wherein one or more products at alowest level node of said hierarchy are assigned as being a member of acategory at an upper category level node of said hierarchy and include alink to that category level node, and second data representingtransaction records having a plurality of transactions related to aplurality of products; clustering said plurality of products based onsaid plurality of transactions in which a new cluster is generatedrelating to products of said plurality; and updating the predeterminedmerchandise hierarchy representation based on said clustering in whichsaid products of said new cluster are assigned as being members of a newcategory level node, and a new link generated for connecting theproducts and corresponding new category level node, wherein saidclustering comprises: initializing a new membership matrix asrepresenting categories and their member product assignments accordingto a lowest level of said predefined merchandise hierarchy; performing,via a computer simulation, an iterative process to minimize an objectivefunction relating a similarity of complementary information between saidplurality of products, wherein at each iteration, assigning each productto a cluster label such that similar items have similar assignments toupdate said new membership matrix and form a refined merchandisehierarchy that satisfies a consistency constraint based on a ratio ofmutual information representing a difference between the predefinedmerchandise hierarchy and the refined merchandise hierarchy; repeatingsaid initializing and performing at a next upper level until a nexthighest level of said refined merchandise hierarchy is reached; andoutputting said new membership matrix.
 8. The computer program productas claimed in claim 7, wherein said objective function is:${{\min{\sum\limits_{i,{j = 1}}^{N}{W_{ij}{{C_{i} - {C\; j}}}^{2}}}} = {{trace}\left( {{C^{T}\left( {D - W} \right)}C} \right)}},$wherein W={W_(ij)} is an N×N similarity matrix, D=diag{d₁, . . . ,d_(N)}, wherein d_(i)=Σ_(j)W_(ij), C is a N×K new member matrix, whereinC_(i)=ith row of C and Cj=jth row of C, C^(T)is a transpose matrix of C,N is a number of products in a current level of said predeterminedmerchandise hierarchy, and K is a number of new categories in a currentlevel of said predetermined merchandise hierarchy.
 9. The computerprogram product as claimed in claim 8, wherein said consistencyconstraint based on a ratio of mutual information is computed as:$\mspace{20mu}{{{Q\left( {C,T} \right)} = {{H(T)}/{I\left( {C,T} \right)}}},{{{wherein}\mspace{14mu} H(T)} = {- {\sum\limits_{j = 1}^{M}{p_{j}^{*}\log\left( p_{j}^{*} \right)}}}},\text{}{{{I\left( {C,T} \right)} = {{\sum\limits_{i = 1}^{K}{\sum\limits_{j = 1}^{M}{p_{ij}{\log\left( \frac{p_{ij}}{p_{i}^{*} \times p_{j}^{*}} \right)}}}} = {{the}\mspace{14mu}{mutal}\mspace{14mu}{information}\mspace{14mu}{between}\mspace{14mu} C\mspace{14mu}{and}\mspace{14mu} T}}};}}$and, wherein C is a N×K new member matrix, T is an existing categorylabels matrix defined by the existing hierarchy, p_(ij) is a fraction ofsales volume of products in new category i and existing category j,p_(i)*=Σ_(j)p_(ij)=fraction of sales volume of products in new categoryi p*_(j)=Σ_(i)p_(ij)=fraction of sales volume of products in existingcategory j, N is a number of products in a current level of saidpredetermined merchandise hierarchy, M is a number of originalcategories in a current level of said predetermined merchandisehierarchy, and K is a number of new categories in a current level ofsaid predetermined merchandise hierarchy.
 10. The computer programproduct as claimed in claim 9, wherein said first data representingpredetermined merchandise hierarchy including said tree data structureincludes a top level node, representing a top of said hierarchy, and afirst lower hierarchy level including one or more first lower levelnodes connected to said top node by respective links, and a second lowerhierarchy level including one or more second lower level nodes connectedto a node of said first lower level nodes via links, said updating thepredetermined merchandise hierarchy representation comprising adding anew node and link connecting to a node of said first lower or secondnext lower level node.
 11. The computer program product as claimed inclaim 10, wherein said new membership matrix output includes clusterassignments C used for updating the nodes and links in saidpredetermined merchandise hierarchy representation.
 12. The computerprogram product as claimed in claim 7, wherein said iterative processincludes applying a Genetic Algorithm.